RCMP Const. Kris Clark said that police were called to 9th Street across from Queen Elizabeth Park at about 11:15 a.m. PT Friday morning, where officers found the injured man.
He had life-threatening injuries and was first taken to Queen Victoria Hospital, and later flown to Royal Inland Hospital in Kamloops.
As the investigation progressed, officers discovered that there had apparently been an interaction between the 55-year-old man and another man, a 33-year-old, on the roadway in front of the park.
Police continue to investigate how the 55-year-old man sustained his injuries, and are urging anyone with information to call Revelstoke RCMP at 250-837-5255 or Crime Stoppers at 1-800-222-8477.
As of Saturday evening, the injured man was still in critical condition, Clark said.
His identity is not being released as family-member notification is ongoing.
Revelstoke is a city of roughly 7,200, and is approximately 200 kilometres east of Kamloops.